By Caren Bohan

WASHINGTON, Sept 13 (Reuters) - President George W. Bush's offer of a limited U.S. troop cut will probably buy time for his Iraq strategy but analysts said his upbeat portrayal of conditions there may come back to haunt him.

Bush told Americans in a televised address that forces in Iraq could be cut by about 20,000 by next July and he linked the reduction to what he said was progress on the ground, especially in volatile Anbar province and even in Baghdad.

He also hinted at the possibility of a larger drawdown, saying, "the more successful we are, the more American troops can return home."

The speech was part of an orchestrated roll-out of events, including Bush's surprise trip to Iraq and the testimony of his top commander, Gen. David Petraeus, that could well give the president the upper hand in his fight with a Democratic-led Congress that wants a much faster withdrawal.

But the goal of bringing stability to Iraq and reconciling the country's warring factions may prove far more elusive, experts said.

"The strategy is a very high-risk one," James Dobbins, a former Bush administration envoy to Afghanistan, said of U.S. efforts to engage Sunni tribal leaders and Shi'ite militias while prodding the weak central government to meet political benchmarks.

"If it doesn't work, it is a prescription for a much more bloody civil war. On the other hand, the United States doesn't have any more low-risk options left in Iraq," added Dobbins, who is now an analyst with the RAND think tank.

ROSY PICTURE

Long accused of painting an overly rosy picture of the war in Iraq, Bush relied heavily on the aura of competence of Petraeus and the U.S. ambassador to Iraq, Ryan Crocker, to make the case that hopeful signs were emerging.

But Dobbins said that while Petraeus was able to argue that the United States was achieving some tactical successes, neither he nor Crocker was able to make a convincing case that the United States was achieving the broader strategic goal of political reconciliation.

Christopher Gelpi, political science professor at Duke University, said Petraeus' testimony amounted to "cherry-picking" the facts to make the case for progress.

Gelpi noted that several recent reports, including one from a congressional watchdog agency last week, offered far grimmer assessments.

Still, Gelpi said that the testimony from Petraeus and Crocker was effective enough that it may stem defections by lawmakers in Bush's own Republican party and could prevent Democrats from having the votes to force Bush's hand.

"It seems likely to me that the president has rescued enough votes in Senate to block any substantial change in policy," Gelpi said.

While Democrats control both the House of Representatives and the Senate, the Senate is closely divided between Republicans and Democrats.

The decline of 20,000 in U.S. troop levels that Bush promised by July -- and focused on in his speech -- would effectively reverse the buildup he ordered at the start of this year. But a reduction of that size has long been expected to occur sometime in 2008.

Extra units deployed for the so-called surge need to be rotated out of Iraq between next April and August to prevent further strains on the military from extended deployments.

Bush gave no specifics on a time frame for any troop cuts beyond mid-2008 and indeed said he thought it was important that the United States maintain a "security engagement" in Iraq that extends beyond the end of his presidency in January 2009.

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